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<p>Zero-or-one inflated (ZOI) proportional data, common in various fields, presents modelling challenges due to significant zeros and ones. We propose a three-part mixture distribution model that combines degenerate distributions at zero and one with a unit-Weibull distribution for the (0,1) interval. Quantile regression is employed instead of mean regression to capture the global distribution of response variables. Bayesian variational inference, specifically Gaussian variational approximation with a factorized covariance structure, is used for parameter estimation, offering computational efficiency over traditional methods. Bayesian variable selection is achieved using the Bayesian Lasso. Simulation studies and real data analyses demonstrate the effectiveness of the proposed method in parameter estimation and variable selection.</p>

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Gaussian variational approximation for Bayesian Lasso quantile regression model with zero-or-one inflated proportional data

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Zhiqiang Wang,
  • Ying Wu

摘要

Zero-or-one inflated (ZOI) proportional data, common in various fields, presents modelling challenges due to significant zeros and ones. We propose a three-part mixture distribution model that combines degenerate distributions at zero and one with a unit-Weibull distribution for the (0,1) interval. Quantile regression is employed instead of mean regression to capture the global distribution of response variables. Bayesian variational inference, specifically Gaussian variational approximation with a factorized covariance structure, is used for parameter estimation, offering computational efficiency over traditional methods. Bayesian variable selection is achieved using the Bayesian Lasso. Simulation studies and real data analyses demonstrate the effectiveness of the proposed method in parameter estimation and variable selection.